my code:
function [e, e_rate, e_flag, ...
rc_sec,rp_sec, ...
a_ck, rou_ck, a_pk, rou_pk, ...
a_ce, rou_ce, a_ke, rou_ke ...
] = ...
e_func(a_ck_iter, rou_ck_iter,a_pk_iter, rou_pk_iter,...
a_ce_iter, rou_ce_iter,a_ke_iter, rou_ke_iter,...
UE, PE, N, M, G_U, G_E, w_ini, rc_sec_iter, rp_sec_iter,e_iter, noise_maxpower, trans_maxpower, miu_t, miu_r,miu_e)
% wc * wc'
WC = w_ini(1:N) * w_ini(1:N)';
% wi * wi'
for i = 1 : UE
W(:,:,i) = w_ini(N*i+1:N*(i+1)) * w_ini(N*i+1:N*(i+1))';
end
% w1*w1' + w2*w2' + ...
WS = zeros(N,N);
for i = 1 : UE
WS = WS + W(:,:,i);
end
% diag(wc*wc' + w1*w1' + w2*w2' + ...)
WT = WC + WS;
DIAG_WT = diag(diag(WT));
AWGN_USER = (1 + miu_r) * noise_maxpower;
AWGN_PE = (1 + miu_e) * noise_maxpower;
cvx_solver mosek
% cvx_save_prefs
cvx_begin
variable t
variable e(M) complex
variable a_ck(UE)
variable rou_ck(UE)
variable a_pk(UE)
variable rou_pk(UE)
variable a_ce
variable rou_ce
variable a_ke(UE)
variable rou_ke(UE)
variable deta_rc_sec(UE)
variable deta_rp_sec(UE)
expression constraint(UE * (2 + 2 + 1 + 2));
expression LEFT_CK(UE);
expression RIGHT_CK(UE);
for i = 1 : UE
A(:,:,i) = G_U(:,:,i) * WS * G_U(:,:,i)' + miu_r * G_U(:,:,i) * WT * G_U(:,:,i)' + miu_t * (1 + miu_r) * G_U(:,:,i) * DIAG_WT * G_U(:,:,i)';
LEFT_CK(i) = quad_form([e;1],A(:,:,i));
LEFT_CK(i) = LEFT_CK(i) + AWGN_USER;
RIGHT_CK(i) = 2 * real(e_iter' * (G_U(:,:,i) * WC * G_U(:,:,i)') * [e;1]) / rou_ck_iter(i) - (e_iter' * (G_U(:,:,i) * WC * G_U(:,:,i)') * e_iter) * rou_ck(i) / rou_ck_iter(i)^2;
constraint((i -1 ) * 2 + 1) = exp(log(2)*a_ck(i)) - rou_ck(i) - 1;
constraint((i - 1) * 2 + 2) = LEFT_CK(i) - real(RIGHT_CK(i));
end
expression LEFT_PK(UE);
expression RIGHT_PK(UE);
bob = i * 2;
for i = 1 : UE
B(:,:,i) = G_U(:,:,i) * (WS-W(:,:,i)) * G_U(:,:,i)' + miu_r * G_U(:,:,i) * WT * G_U(:,:,i)' + miu_t * (1 + miu_r) * G_U(:,:,i) * DIAG_WT * G_U(:,:,i)';
LEFT_PK(i) = quad_form([e;1],B(:,:,i));
LEFT_PK(i) = LEFT_PK(i) + AWGN_USER;
RIGHT_PK(i) = 2 * real(e_iter' * (G_U(:,:,i) * W(:,:,i) * G_U(:,:,i)') * [e;1]) / rou_pk_iter(i) - (e_iter' * (G_U(:,:,i) * W(:,:,i) * G_U(:,:,i)') * e_iter) * rou_pk(i) / rou_pk_iter(i)^2;
constraint(bob + (i - 1) * 2 + 1) = exp(log(2)*a_pk(i)) - rou_pk(i) - 1;
constraint(bob + (i - 1) * 2 + 2) = LEFT_PK(i) - real(RIGHT_PK(i));
end
expression LEFT_CE;
expression RIGHT_CE;
tom = bob + i * 2;
POP_CORN = (G_E(:,:,1) * WS * G_E(:,:,1)' + miu_e * G_E(:,:,1) * WT * G_E(:,:,1)' + miu_t * (1 + miu_e) * G_E(:,:,1) * DIAG_WT * G_E(:,:,1)');
LEFT_CE = quad_over_lin(w_ini(1:N)' * G_E(:,:,1)' * [e;1] , rou_ce);
RIGHT_CE = 2 * real(e_iter' * POP_CORN * [e;1]) - e_iter' * POP_CORN * e_iter;
RIGHT_CE = RIGHT_CE + AWGN_PE;
constraint(tom + 1) = 1 + rou_ce - (2^a_ce_iter) * (1 + log(2) * (a_ce - a_ce_iter));
constraint(tom + 2) = LEFT_CE - real(RIGHT_CE);
expression LEFT_KE(UE);
expression RIGHT_KE(UE);
jerry = tom + 2;
for i = 1 : UE
COCA_COLA = (G_E(:,:,1) * WC * G_E(:,:,1)' + G_E(:,:,1) * (WS -W(:,:,i)) * G_E(:,:,1)' + miu_e * G_E(:,:,1) * WT * G_E(:,:,1)' + miu_t * (1 + miu_e) * G_E(:,:,1) * DIAG_WT * G_E(:,:,1)');
LEFT_KE(i) = quad_over_lin(w_ini(N*i+1:N*(i+1))' * G_E(:,:,1)' * [e;1] , rou_ke(i));
RIGHT_KE(i) = 2 * real(e_iter' * COCA_COLA * [e;1]) - e_iter' * COCA_COLA * e_iter;
RIGHT_KE(i) = RIGHT_KE(i) + AWGN_PE;
constraint(jerry + (i-1) * 2 + 1) = 1 + rou_ke(i) - (2^a_ke_iter(i)) * (1 + log(2) * (a_ke(i) - a_ke_iter(i)));
constraint(jerry + (i-1) * 2 + 2) = LEFT_KE(i) - real(RIGHT_KE(i));
end
expression bat(M);
for i = 1 : M
bat(i) = real(2 * real(e_iter(i)' * e(i)) - e_iter(i)' * e_iter(i) - 1);
end
punish = 0.001 * sum(bat);
maximize t + punish
subject to
real(constraint)<=0;
deta_rc_sec >= 0;
for i = 1 : UE
sum(rc_sec_iter + deta_rc_sec) <= a_ck(i) - a_ce;
end
deta_rp_sec >= 0;
for i = 1 : UE
rp_sec_iter(i) + deta_rp_sec(i) <= a_pk(i) - a_ke(i);
end
for i = 1 : UE
t <= rc_sec_iter(i) + deta_rc_sec(i) + rp_sec_iter(i) + deta_rp_sec(i);
end
for i = 1 : M
abs(e(i)) <= 1;
end
cvx_end
if cvx_status(1) == 'S' || cvx_status(3) == 'a'
e_flag=1;
e_rate= t;
rc_sec = rc_sec_iter + deta_rc_sec;
rp_sec = rp_sec_iter + deta_rp_sec;
else
e_flag=0;
e_rate=0;
e =ones(M,1);
rc_sec = 0;
rp_sec = 0;
a_ck = 0; rou_ck = 0; a_pk = 0; rou_pk = 0;
a_ce = 0; rou_ce = 0; a_ke = 0; rou_ke = 0;
end
Initial value of the second iteration：
w_ini：[7.821536513305144;4.857147214044837;3.229928731498855;2.159048879292589;0.319566135187890;0.188763447956598]
a_ck_iter：[2.412311953582665;2.387308638191314]
rou_ck_iter：[4.414149368022386;4.231804972481462]
a_ce_iter：9.234578309612607e-04
rou_ce_iter：6.402883441407603e-04
a_ke_iter：[0.005749652015342;4.647295573870919e-05]
rou_ke_iter：[0.003993251679489;3.221209737025443e-05]
a_pk_iter：[2.382036497372875;0.010046284505766]
rou_pk_iter：[4.212720671821359;0.006987856195515]
cvx information
Calling Mosek 9.1.9: 108 variables, 52 equality constraints
------------------------------------------------------------
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 52
Cones : 21
Scalar variables : 108
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.06
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 52
Cones : 21
Scalar variables : 108
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 38
Optimizer - Cones : 21
Optimizer - Scalar variables : 95 conic : 78
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 485 after factor : 511
Factor - dense dim. : 0 flops : 3.39e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.5e+00 1.3e+00 1.4e+01 0.00e+00 0.000000000e+00 -1.322040801e+01 1.0e+00 0.13
1 9.8e-01 5.0e-01 4.2e+00 2.86e-01 2.862260641e-01 -6.241498296e+00 3.9e-01 0.34
2 2.3e-01 1.2e-01 5.9e-01 5.73e-01 2.844738315e-01 -1.548555358e+00 9.0e-02 0.34
3 1.0e-01 5.2e-02 1.7e-01 7.30e-01 8.884936453e-02 -7.630662992e-01 4.0e-02 0.36
4 4.2e-02 2.1e-02 5.0e-02 8.39e-01 3.934978891e-02 -3.388302640e-01 1.7e-02 0.38
5 7.8e-03 4.0e-03 4.2e-03 9.15e-01 -9.410744853e-03 -8.237378954e-02 3.1e-03 0.38
6 2.0e-03 1.0e-03 5.5e-04 1.01e+00 -1.692712855e-02 -3.525538640e-02 8.0e-04 0.39
7 4.8e-04 2.5e-04 6.7e-05 1.00e+00 -1.917175232e-02 -2.356871084e-02 1.9e-04 0.41
8 1.5e-04 7.6e-05 1.2e-05 9.68e-01 -1.974897272e-02 -2.111299496e-02 5.9e-05 0.41
9 2.8e-05 1.4e-05 8.4e-07 1.07e+00 -1.997054986e-02 -2.021776659e-02 1.1e-05 0.42
10 7.6e-06 3.9e-06 9.3e-08 1.34e+00 -2.000697730e-02 -2.006310827e-02 3.0e-06 0.42
11 3.0e-06 1.6e-06 2.4e-08 1.25e+00 -2.003045994e-02 -2.005119989e-02 1.2e-06 0.44
12 3.2e-07 1.7e-07 9.2e-10 1.01e+00 -2.005323362e-02 -2.005542001e-02 1.3e-07 0.45
13 1.4e-07 7.3e-08 4.1e-10 5.94e-01 -2.005245067e-02 -2.005383783e-02 5.7e-08 0.47
14 8.8e-08 3.4e-08 2.4e-10 -2.51e-01 -2.004937146e-02 -2.005045206e-02 2.7e-08 0.47
15 4.5e-08 1.8e-08 1.2e-10 -1.10e-01 -2.004600761e-02 -2.004671341e-02 1.4e-08 0.48
16 4.5e-08 1.8e-08 1.2e-10 -9.96e-02 -2.004600761e-02 -2.004671341e-02 1.4e-08 0.50
17 4.5e-08 1.8e-08 1.2e-10 -9.72e-02 -2.004600761e-02 -2.004671341e-02 1.4e-08 0.50
18 3.5e-08 8.8e-09 4.6e-11 5.30e-01 -2.005107611e-02 -2.005146300e-02 6.6e-09 0.52
19 1.1e-08 9.7e-10 5.8e-12 -2.06e-01 -2.004803699e-02 -2.004792089e-02 1.2e-09 0.53
20 6.7e-09 5.1e-10 3.1e-12 -1.48e-01 -2.004577881e-02 -2.004558883e-02 6.8e-10 0.55
21 6.7e-09 5.1e-10 3.1e-12 1.09e-01 -2.004577881e-02 -2.004558883e-02 6.8e-10 0.55
22 5.4e-09 2.7e-11 4.0e-14 1.08e+00 -2.004955185e-02 -2.004954092e-02 5.1e-10 0.56
23 5.0e-09 2.5e-11 4.3e-14 5.21e-02 -2.004940146e-02 -2.004938386e-02 4.7e-10 0.56
24 4.8e-09 2.5e-11 4.3e-14 5.30e-02 -2.004893128e-02 -2.004891217e-02 4.6e-10 0.59
25 4.7e-09 2.4e-11 4.3e-14 -2.74e-01 -2.004878727e-02 -2.004876727e-02 4.5e-10 0.59
26 4.1e-09 2.0e-10 3.4e-14 1.98e+00 -2.004602224e-02 -2.004595589e-02 3.8e-10 0.61
27 3.6e-09 1.8e-10 3.0e-14 -1.48e-01 -2.004505842e-02 -2.004498912e-02 3.4e-10 0.61
28 3.6e-09 1.8e-10 3.0e-14 1.97e-01 -2.004504493e-02 -2.004497567e-02 3.4e-10 0.64
29 3.6e-09 1.8e-10 3.0e-14 -3.86e-01 -2.004504493e-02 -2.004497567e-02 3.4e-10 0.64
30 3.6e-09 1.8e-10 3.0e-14 1.00e+00 -2.004504493e-02 -2.004497567e-02 3.4e-10 0.66
31 3.6e-09 1.8e-10 3.0e-14 1.00e+00 -2.004504445e-02 -2.004497519e-02 3.4e-10 0.67
Optimizer terminated. Time: 0.80
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -2.0045044448e-02 nrm: 9e+02 Viol. con: 9e-05 var: 0e+00 cones: 0e+00
Dual. obj: -2.0044975189e-02 nrm: 5e+01 Viol. con: 0e+00 var: 5e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.80
Interior-point - iterations : 32 time: 0.67
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +2.38633
Calling Mosek 9.1.9: 108 variables, 52 equality constraints
------------------------------------------------------------
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 52
Cones : 21
Scalar variables : 108
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.03
Lin. dep. - number : 0
Presolve terminated. Time: 0.06
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 52
Cones : 21
Scalar variables : 108
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 38
Optimizer - Cones : 21
Optimizer - Scalar variables : 95 conic : 78
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 485 after factor : 511
Factor - dense dim. : 0 flops : 3.39e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.5e+00 1.3e+00 1.4e+01 0.00e+00 0.000000000e+00 -1.322040801e+01 1.0e+00 0.13
1 9.8e-01 5.0e-01 4.2e+00 2.86e-01 2.863613140e-01 -6.240313907e+00 3.9e-01 0.34
2 2.3e-01 1.2e-01 5.9e-01 5.73e-01 2.844502251e-01 -1.543771426e+00 9.0e-02 0.34
3 1.0e-01 5.2e-02 1.7e-01 7.30e-01 8.848339507e-02 -7.604587294e-01 4.0e-02 0.36
4 4.2e-02 2.1e-02 5.0e-02 8.39e-01 3.917456071e-02 -3.380322650e-01 1.7e-02 0.38
5 7.9e-03 4.0e-03 4.2e-03 9.15e-01 -9.440625376e-03 -8.238834207e-02 3.1e-03 0.38
6 2.0e-03 1.0e-03 5.5e-04 1.01e+00 -1.692441860e-02 -3.525720214e-02 8.0e-04 0.39
7 4.8e-04 2.5e-04 6.7e-05 9.99e-01 -1.915754492e-02 -2.358191744e-02 1.9e-04 0.41
8 1.5e-04 7.7e-05 1.2e-05 9.51e-01 -1.972866212e-02 -2.112319692e-02 5.9e-05 0.41
9 2.5e-05 1.3e-05 8.0e-07 1.02e+00 -1.995911314e-02 -2.019381116e-02 1.0e-05 0.42
10 6.3e-06 3.2e-06 8.4e-08 1.16e+00 -1.999632116e-02 -2.004990879e-02 2.5e-06 0.44
11 2.0e-06 1.0e-06 1.3e-08 1.37e+00 -2.000395834e-02 -2.001803738e-02 7.9e-07 0.45
12 5.9e-07 3.0e-07 2.2e-09 1.09e+00 -2.001532606e-02 -2.001942930e-02 2.3e-07 0.47
13 2.0e-07 1.0e-07 5.8e-10 7.98e-01 -2.001693722e-02 -2.001860028e-02 8.1e-08 0.48
14 1.3e-07 6.9e-08 4.5e-10 -9.09e-03 -2.001464981e-02 -2.001626374e-02 6.6e-08 0.48
15 5.8e-08 3.0e-08 2.2e-10 -1.78e-01 -2.001006566e-02 -2.001110887e-02 2.9e-08 0.50
16 4.3e-08 2.2e-08 1.8e-10 -7.44e-01 -2.000794797e-02 -2.000882073e-02 1.9e-08 0.52
17 1.0e-08 4.9e-09 4.0e-11 -6.81e-02 -1.999952069e-02 -1.999958751e-02 4.1e-09 0.52
18 9.6e-09 4.5e-09 3.9e-11 -4.58e-01 -1.999962837e-02 -1.999965277e-02 3.8e-09 0.53
19 5.3e-09 1.4e-09 2.5e-11 -5.11e-01 -2.000072608e-02 -1.999904656e-02 1.2e-09 0.55
20 2.6e-09 6.3e-10 8.5e-12 5.62e-01 -1.999662910e-02 -1.999559788e-02 7.9e-10 0.55
21 1.6e-09 1.5e-10 6.1e-13 -9.81e-01 -1.897681043e-02 -1.848561853e-02 3.1e-12 0.56
22 6.6e-12 1.1e-10 2.6e-14 -1.00e+00 4.901862193e-01 7.350572286e-01 6.2e-15 0.58
23 1.4e-14 1.3e-10 2.4e-14 -1.00e+00 2.563096064e+02 3.793385085e+02 1.2e-17 0.58
Optimizer terminated. Time: 0.70
Interior-point solution summary
Problem status : ILL_POSED
Solution status : PRIMAL_ILLPOSED_CER
Dual. obj: 7.0516666284e-08 nrm: 1e+01 Viol. con: 0e+00 var: 2e-10 cones: 0e+00
Optimizer summary
Optimizer - time: 0.70
Interior-point - iterations : 23 time: 0.59
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaN